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Special Cube Complexes

- Frédéric Haglund, D. Wise
- MathematicsThe Structure of Groups with a Quasiconvex…
- 2008

Abstract.We introduce and examine a special class of cube complexes. We show that special cube-complexes virtually admit local isometries to the standard 2-complexes of naturally associated… Expand

The Structure of Groups with a Quasiconvex Hierarchy

- D. Wise
- Mathematics
- 1 October 2009

Let $G$ be a word-hyperbolic group with a quasiconvex hierarchy.
We show that $G$ has a finite index subgroup $G'$ that embeds as a
quasiconvex subgroup of a right-angled Artin group.
It follows… Expand

From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry

- D. Wise
- Mathematics
- 28 November 2012

This book presents an introduction to the geometric group theory associated with nonpositively curved cube complexes. It advocates the use of cube complexes to understand the fundamental groups of… Expand

A boundary criterion for cubulation

- N. Bergeron, D. Wise
- Mathematics
- 25 August 2009

We give a criterion in terms of the boundary for the existence of a proper cocompact action of a word-hyperbolic group on a ${\rm CAT}(0)$ cube complex. We describe applications towards lattices and… Expand

Cubulating small cancellation groups

- D. Wise
- Mathematics
- 1 February 2004

AbstractWe study the B(6) and B(4)-T(4) small cancellation groups.
These classes include the usual C’(1/6) and C’(1/4)-T(4) metric small
cancellation groups. We show that every finitely presented… Expand

Packing subgroups in relatively hyperbolic groups

Our main result establishes the bounded packing of relatively quasiconvex subgroups of a relatively hyperbolic group, under mild hypotheses. As an application, we prove that relatively quasiconvex… Expand

Mixed 3-manifolds are virtually special

- P. Przytycki, D. Wise
- Mathematics
- 30 May 2012

LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that π1M is virtually special.

Non-positively curved squared complexes aperiodic tilings and non-residually finite groups

- D. Wise
- Mathematics
- 1996

A combination theorem for special cube complexes

- Frédéric Haglund, D. Wise
- Mathematics
- 1 November 2012

We prove that certain compact cube complexes have special nite covers. This means they have nite covers whose fundamental groups are quasiconvex subgroups of right-angled Artin groups. As a result we… Expand

Cubulating random groups at density less than 1/6

- Y. Ollivier, D. Wise
- Mathematics
- 28 March 2011

We prove that random groups at density less than 1/6 act freely and cocompactly on CAT(0) cube complexes, and that random groups at density less than 1/5 have codimension-1 subgroups. In particular,… Expand

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